14 citations · 27 across the 10 of their papers we have counts for
11 papers
Phase-Shifted Nanopteron Solutions to a Singularly Perturbed Korteweg--de Vries Equation
Timothy E. Faver
We construct nanopteron solutions to the differential equation \[ ε^2u^{(4)}+u''-u+u^2 =0, \] which is a singular perturbation of the traveling wave problem for the K…
Small-amplitude periodic traveling waves in dimer Fermi-Pasta-Ulam-Tsingou lattices
Timothy E. Faver, Hermen Jan Hupkes, J. Douglas Wright
We prove the existence of small-amplitude periodic traveling waves in dimer Fermi-Pasta-Ulam-Tsingou (FPUT) lattices without assumptions of physical symmetry. Such lattices are inf…
Mass and spring dimer Fermi-Pasta-Ulam-Tsingou nanopterons with exponentially small, nonvanishing ripples
Timothy E. Faver, Hermen Jan Hupkes
We study traveling waves in mass and spring dimer Fermi-Pasta-Ulam-Tsingou (FPUT) lattices in the long wave limit. Such lattices are known to possess nanopteron traveling waves in…
Scaling Relations for Auxin Waves
Timothy E. Faver, Hermen Jan Hupkes, Roeland M. H. Merks +1
We analyze an 'up-the-gradient' model for the formation of transport channels of the phytohormone auxin, through auxin-mediated polarization of the PIN1 auxin transporter. We show…
Micropterons, Nanopterons and Solitary Wave Solutions to the Diatomic Fermi-Pasta-Ulam-Tsingou Problem
Timothy E. Faver, Hermen Jan Hupkes
We use a specialized boundary-value problem solver for mixed-type functional differential equations to numerically examine the landscape of traveling wave solutions to the diatomic…
Solitary Waves in Mass-in-Mass Lattices
Timothy E. Faver, Roy H. Goodman, J. Douglas Wright
We consider the existence of spatially localized traveling wave solutions of the mass-in-mass lattice. Under an anti-resonance condition first discovered by Kevrekidis, Stefanov an…